Robust preconditioners for a new stabilized discretization of the poroelastic equations

J. H. Adler, F. J. Gaspar, X. Hu, P. Ohm, C. Rodrigo, L. T. Zikatanov

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3 Scopus citations

Abstract

In this paper, we present block preconditioners for a stabilized discretization of the poroelastic equations developed in [C. Rodrigo, X. Hu, P. Ohm, J. Adler, F. Gaspar, and L. Zikatanov, Comput. Methods Appl. Mech. Engrg., 341 (2018), pp. 467-484]. The discretization is proved to be well-posed with respect to the physical and discretization parameters and thus provides a framework to develop preconditioners that are robust with respect to such parameters as well. We construct both norm-equivalent (diagonal) and field-of-value-equivalent (triangular) preconditioners for both the stabilized discretization and a perturbation of the stabilized discretization, which leads to a smaller overall problem after static condensation. Numerical tests for both two-and three-dimensional problems confirm the robustness of the block preconditioners with respect to the physical and discretization parameters.

Original languageEnglish (US)
Pages (from-to)B761-B791
JournalSIAM Journal on Scientific Computing
Volume42
Issue number3
DOIs
StatePublished - 2020

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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